Finite and Infinitesimal Damage: Study of Evolution and Experimental Simulation

Abstract

The damage-related internal variables are introduced as associated with kinematical (deformation) measures. Two basic damage tensors relative to finite damage are defined through macro-micro transition for the Lagrangian velocity gradient and the Eulerian one. Both reduce to a small-damage tensor as the finite deformation measures reduce to their common infinitesimal strain counterpart. The damage mechanism by cavity growth from hard inclusions is examined. The systematic procedure is proposed to settle up the damage evolution equation. It is based on the datum of the local velocity field within an elementary cell viewed as an element containing an inner cavity and subject to displacement boundary conditions compatible with homogeneous deformation of outer faces. Experimental procedure is employed to verify the hypotheses regarding the local velocity field in the cell and evolutive cavity forms in a two-dimensional case. Artificial cylindrical inclusions are embedded in a metal plate, periodicity of their spacing being respected. The laser-speckle measurements of displacement increments are performed within a unit-cell chosen as the whole element is loaded to plasticity range. They permit to evaluate the “local” smoothed velocity field perturbed by cavity presence.